Their proposal received a cautious welcome from Scottish Women’s Aid yesterday.

A spokeswoman said: “This discussion must include women and children who have experienced domestic abuse in order to consider whether monitoring could be used safely and appropriately.

“Electronic monitoring must not be considered as an alternative to remanding persistent and dangerous perpetrators.”

Massachusetts pioneered the use of GPS tracking in domestic violence cases in 2009 and it is now used in another 12 states.

A US Department of Justice report concluded: “Victims largely felt that having defendants on GPS during the pretrial period provided relief from the kind of abuse suffered prior to GPS.”

Officers in Scotland also want to use the trackers to monitor repeat offenders, especially those convicted of sexual assaults.

They hope it could stop beasts such as Ryan Yates, a 34-year-old paedophile who tried to kill a woman and abduct her two grandchildren in Bridge of Don, Aberdeen, just five days after being released from prison in 2009.

Big Brother Watch director Nick Pickles said: “Requiring someone to wear these trackers should be approved by a court and not be allowed to become a routine option for lazy policing.

“Technology is never perfect and this isn’t a magic solution to protecting victims.”

The Scottish Government said they were “analysing” Police Scotland’s proposal.